Nontrivial solutions for a $(p,q)$-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912175802548224 |
|---|---|
| author | Yu, Zhangyi Xie, Junping Zhang, Xingyong |
| author_facet | Yu, Zhangyi Xie, Junping Zhang, Xingyong |
| contents | By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation terms on a locally weighted and connected finite graph $G=(V,E)$.We also present a necessary condition of the existence of semi-trivial solutions for the system. Moreover, by using Ekeland's variational principle and Clark's Theorem, respectively, we prove that the system has at least one or multiple semi-trivial solutions when the perturbation terms satisfy different assumptions. Finally, we present a nonexistence result of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nontrivial solutions for a $(p,q)$-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs Yu, Zhangyi Xie, Junping Zhang, Xingyong Analysis of PDEs By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation terms on a locally weighted and connected finite graph $G=(V,E)$.We also present a necessary condition of the existence of semi-trivial solutions for the system. Moreover, by using Ekeland's variational principle and Clark's Theorem, respectively, we prove that the system has at least one or multiple semi-trivial solutions when the perturbation terms satisfy different assumptions. Finally, we present a nonexistence result of solutions. |
| title | Nontrivial solutions for a $(p,q)$-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.02041 |